CUMULATE asymptotic knowledge assessment: Difference between revisions
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==Computation== | ==Computation== | ||
The formula below is used to update the knowledge levels of concepts (c) addressed in a problem (p) | The formula below is used to update the knowledge levels of concepts (c) addressed in a problem (p). This formula reflects the following principles. | ||
* there are several domain concepts (knowledge items, rules, productions) involved in solving a problem; the knowledge of each of them is updated proportionally to the others | |||
* knowledge is updated only upon correct user answers, there is no penalty for errors | |||
* solving a problem correctly multiple times will result in diminishing update (growth) of the knowledge level of the concepts as the number of successes grows | |||
[[Image:CUMULATE asymptotic knowledge assessment.png]], where | [[Image:CUMULATE asymptotic knowledge assessment.png]], where | ||
* Ko - is the starting level of knowledge (here we always start from 0) | * Ko - is the starting level of knowledge (here we always start from 0) | ||
* res - result of user action (0 -error, 1 - correct); | * res - result of user action (0 -error, 1 - correct); | ||
* Wc,p - is a weight of concept c in problem p | * Wc,p - is a weight of concept c in problem p | ||
* ΣWc,p - is the sum of weights of all concepts in problem p | * ΣWc,p - is the sum of weights of all concepts in problem p | ||
* <sub>succ</sub>att<sub>p</sub> - is a number of successful solutions to problem p prior to current attempt | * <sub>succ</sub>att<sub>p</sub> - is a number of successful solutions to problem p prior to current attempt | ||
Revision as of 19:34, 8 April 2009
Asymptotic knowledge assessment is CUMULATE's legacy user modeling algorithm for computing user knowledge with respect to problem-solving.
Computation
The formula below is used to update the knowledge levels of concepts (c) addressed in a problem (p). This formula reflects the following principles.
- there are several domain concepts (knowledge items, rules, productions) involved in solving a problem; the knowledge of each of them is updated proportionally to the others
- knowledge is updated only upon correct user answers, there is no penalty for errors
- solving a problem correctly multiple times will result in diminishing update (growth) of the knowledge level of the concepts as the number of successes grows
, where
- Ko - is the starting level of knowledge (here we always start from 0)
- res - result of user action (0 -error, 1 - correct);
- Wc,p - is a weight of concept c in problem p
- ΣWc,p - is the sum of weights of all concepts in problem p
- succattp - is a number of successful solutions to problem p prior to current attempt